بوابة الثانوية العامة المصرية - عرض مشاركة واحدة

einstien · #12 13-08-2011, 05:30 PM

$sin x + cos x = 1 \Rightarrow sin x = 1-cos x (by squaring the two sides )\Rightarrow sin^{2}x = 1 - 2 cosx +cos^{2}x\Rightarrow 1- cos^{2}x = 1 - 2cos x+cos^{2}x\Rightarrow 2cos^{2}x - 2 cos x = zero \Rightarrow cos^{2}x - cos x = zero \Rightarrow cosx(cosx - 1)=zero \Rightarrow cosx = zero \Rightarrow x = \pi / 2 + 2 \pi k OR x = -\pi /2 + 2\pi k(refused)(the second case) / cos x = 1 \Rightarrow x = 2\pi + 2 \pi k \forall k\epsilon \mathbb{Z}$